Yes, a heater core can help with over heating. It is part of the system. If the water isnt flowing like it should, then the car will over heat.
Have the radiator rotted out. This will clean the insides out. Rust scale is usually what blocks a radiator up. If it has the org heater core, now would be a good time to replace it. check out
www.rockauto.com for a price on one.
Always use distilled water, and I like to add water wetter. The stuff works.